He actually wasn't that bloodthirsty for a republican who was buddy buddy with Kissinger, and who served under Reagan, Nixon, and Bush. He's one of those 'sensible' republicans - a true game player.
In April 2003 when Bush started talking military action on Syria or Iran, Eagleburger said that public opinion would not support such a move and that "If President Bush were to try it now, even I would feel he should be skinned alive."
The funniest thing about him is that he has three sons, all called Lawrence Eagleburger. Seriously. When questioned as to why, he said it was for ego, and to fuck with social security.